| 一类无处可微连续函数的构造及其几何性质 |
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| 引用本文： | 吕冬梅,王宏勇. 一类无处可微连续函数的构造及其几何性质[J]. 淮北煤炭师范学院学报(自然科学版), 2000, 0(1) |
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| 作者姓名： | 吕冬梅 王宏勇 |
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| 作者单位： | 淮北煤师院附中!安徽淮北235000(吕冬梅)，淮北煤师院数学系!安徽淮北235000(王宏勇) |
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| 摘 要： | 借助于实数的Ｃａｎｔｏｒ级数表达式．在单位区间上构造了一类用二进小数表示的函数．证明了这类函数是处处连续但处处不可微的．并且在一定的条件下．讨论了这类函数的几何对称性．
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| 关 键 词： | Cantor级数 无处可微连续函数 对称性 |
Construction and Geometrical Properties of a Class of Nowhere Differentiable Continuous Functions |
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| L Dong-mei, WANG Hong-yong. Construction and Geometrical Properties of a Class of Nowhere Differentiable Continuous Functions[J]. Journal of Huaibei Coal Industry Teachers College(Natural Science edition), 2000, 0(1) |
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| Authors: | L Dong-mei WANG Hong-yong |
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| Abstract: | In this paper, a class of nowhere differentiable continuous functions on the unit interval are constructed by means of the Cantor series expressions of real numbers. Moreover, under a certain condition, the geometrical properties of these functions are also discussed. |
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| Keywords: | Cantor series nondifferentiable continuous functions symmetry |
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